Equations and algorithm for Reverse Osmosis systems normalization

Equations and algorithm for Reverse Osmosis systems normalization

On this page you will find a normalization algorithm that can be built in the PLC or in a SCADA system, therefore eliminating the need of the spreadsheets. This algorithm will deliver the normalized results in three variables: Pressure Drop, Permeability and Salt Passage rate. It also can consider the Concentration Polarization factor for a higher precision.

Normalization is a conversion of operational data that allows the user to compare operation at a specific set of conditions to a reference set of conditions in Reverse Osmosis plants. This allows the user to determine whether changes in flow or rejection are caused by fouling, damage to the membrane, or are just due to different operating conditions: temperature, flow and recovery changes and feed water salinity variations.

The RO normalization equations are described in the ASTM D 4516 (2010) and most membrane manufactures distribute free spreadsheets that have slightly improved calculations over the described in the ASTM.

RO and NF membranes can be defined by two parameters known in the industry as A and B-values. The

A-Value represents the water permeability or the resulting flux from a specific driving pressure. The A-value is directly proportional to the Normalized Permeate Flow, most manufacturers recommend cleaning the membranes when those parameters drop 10% from the stabilized startup reference. A lower A-Value after a few months of operation most likely is an indication of fouling. A-Value is measured in GFD/psi or LMH/bar, in the International System: m²/(m².s.Pa).

B-Value is the salt diffusion rate through the membrane. Every salt has it's own B-value for a specific membrane according to it's chemical and physical properties and the Normalization model considers all salts as if they were NaCl. The B-value is directly proportional to the Normalized Salt Rejection, most manufacturers recommend cleaning the modules when those parameters increase 10%. A higher B-Value after a few months of operation might indicate fouling or membrane degradation (abrasion, oxidation, etc...). B-Value is measured in flux units: GFD or LMH, in the International System: m³/(m².s).

Why use permeability and salt diffusion rate and not Normalized Flow and Normalized Rejection?

By using the permeability (A-value) and salt diffusion rate (B-value) we can directly compare different plants and different membranes in the same scale. That's impossible using the ASTM terms since a plant can have a normalized flow of 100m³/h and another of 25m³/h.

This algorithm was implemented in Plutocalc Water so if you just need to compare performance you can try this software that works on any computer and also in mobile phones.

The algorithm can also take into consideration (optional) the concentration polarization factor for higher precision (thanks to LG). Please notice that the Concentration Polarization is not part of the ASTM D 4516 equation set.

Source code and equations

This source code was written in JavaScript but it can easily be ported to Java, C or any other language. If you need to see it in action please check the Plutocalc Water application.